In the literature of IMDP-abstractions for control synthesis for stochastic systems [1]}, [2]}, [3]}, the above problem is solved by abstracting the system via an appropriate IMDP, finding an optimal policy over the constructed IMDP and mapping this policy back to the original system. Nevertheless, as already mentioned in the introduction section, the action set \(\mathcal {A}\)  is, generally, assumed discrete a-priori. To the best of our knowledge, the only exception is [3]}, which keeps the action-space continuous, but the max-min problem of value iteration is carried out using heuristics.
